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How many quantum states are possible for an atomic electron for which n=3? (Answer is not...

How many quantum states are possible for an atomic electron for which n=3?

(Answer is not 8 or 12)

Solutions

Expert Solution

Since quantum states of any electron is described by 4 quantum numbers, n, l, ml and s, So

when n = 3, then

possible values of l = 0, 1, 2

Possible values of ml = -2, -1, 0, 1, 2

Possible value of s = +1/2 or -1/2

So total quantum states which is possible for n = 3 will be

n = 3, l = 0, ml = 0, s = +1/2

n = 3, l = 0, ml = 0, s = -1/2

n = 3, l = 1, ml = -1, s = +1/2

n = 3, l = 1, ml = 0, s = +1/2

n = 3, l = 1, ml = 1, s = +1/2

n = 3, l = 1, ml = -1, s = -1/2

n = 3, l = 1, ml = 0, s = -1/2

n = 3, l = 1, ml = 1, s = -1/2

n = 3, l = 2, ml = -2, s = +1/2

n = 3, l = 2, ml = -1, s = +1/2

n = 3, l = 2, ml = 0, s = +1/2

n = 3, l = 2, ml = 1, s = +1/2

n = 3, l = 2, ml = 2, s = +1/2

n = 3, l = 2, ml = -2, s = -1/2

n = 3, l = 2, ml = -1, s = -1/2

n = 3, l = 2, ml = 0, s = -1/2

n = 3, l = 2, ml = 1, s = -1/2

n = 3, l = 2, ml = 2, s = -1/2

So total possible quantum states = 2 + 6 + 10 = 18

Please Upvote.

genius_generous answered 2 months ago
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